please forgive me for the jigsaw puzzle like photos
have a very old webcam
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3 Answers
1friend please don't waste our time setting the following peices into right position .. just type the jist of the questions in the post or use latex !!
62Question.. latexified
L=\lim_{n\rightarrow \infty}a_{n}\\ M=\lim_{n\rightarrow \infty}b_{n}\\ N=\lim_{n\rightarrow \infty}c_{n}\\
a_{n+1}=1/2(b_n+c_n)\\ c_{n+1}=1/2(a_n+b_n)\\ b_{n+1}=1/2(a_n+c_n)\\
62solution:
a_{n+1}-b_{n+1}=1/2(b_n-a_n)
hence, we get that a_{n}-b_{n}=\left(-1/2\right)^{n}(b_0-a_0)
which tends to zero as n tends to zero..
hence L=M=N
we also know that
a_{n}+b_{n}+c_n=a_{n+1}+b_{n+1}+c_{n+1}
hence we have a_{0}+b_{0}+c_0=a_{n}+b_{n}+c_{n}
hence a and c will be the right answers!
